Problem: A B C If: $ AC = 101$, $ AB = 9x + 4$, and $ BC = 9x + 7$, Find $BC$.
Explanation: From the diagram, we can see that the total length of ${AC}$ is the sum of ${AB}$ and ${BC}$ $ {AB} + {BC} = {AC}$ Substitute in the expressions that were given for each length: $ {9x + 4} + {9x + 7} = {101}$ Combine like terms: $ 18x + 11 = {101}$ Subtract $11$ from both sides: $ 18x = 90$ Divide both sides by $18$ to find $x$ $ x = 5$ Substitute $5$ for $x$ in the expression that was given for $BC$ $ BC = 9({5}) + 7$ Simplify: $ {BC = 45 + 7}$ Simplify to find ${BC}$ : $ {BC = 52}$